blender cloth simulation not simulating properly with collision
Add more loop cuts to the skirt (i.e., with CTRL-R), to make the mesh faces more square.  I added about 5 cuts between each of yours, and it simulates much better now.  It will start to look jumbled at first, but it should straighten out by around frame 40.  This will of course make the mesh much bigger.  You can also do coarser (but still squarish) faces and use a subdivision surface modifier.